Shells with hybrid active-passive damping treatments: modeling and vibration control

• Autor(a) principal: C. M. A. Vasques
• Data de Publicação: 2006
• Outros Autores: J. Dias Rodrigues
• Tipo de documento: Livro
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://hdl.handle.net/10216/69558
• topic: Engenharia mecânica, Engenharia mecânica; Mechanical engineering, Mechanical engineering

This paper concerns the mathematical modeling and finite element (FE) solution of general anisotropic shells with hybrid active-passive damping treatments. A fully-coupled piezo-visco-elastic mathematical model of the shell (host structure) and segmented arbitrarily stacked layers of damping treatments is considered. A discrete layer approach is employed in this work, and the weak form of the governing equations is derived for a single generic layer of the multilayer shell using Hamilton's principle and a mixed (displacement/stresses) definition of the displacement field. First, a fully refined deformation theory of the generic layer, based on postulated out-of-plane shear stress definitions and in the in-plane stresses obtained with a Reissner-Mindlin type shell theory, is outlined. A semi-inverse procedure is used to derive the layer mixed non-linear displacement field, in terms of a blend of the generalized displacements of the Love-Kirchhoff and Reissner-Mindlin theories and of the stress components at the generic layer interfaces. No assumptions regarding the thinness of the shell are considered. Regarding the definition of the electric potential, the direct piezoelectric effects are condensed into the model through effective stiffness and strains definitions, and the converse counterpart is considered by the action of prescribed electric potential differences in each piezoelectric layer. Then, the weak forms of a partially refined theory, where only the zero-order term of the non-linear fully refined transverse displacement is retained, are derived for an orthotropic doubly-curved piezo-elastic generic shell layer. Based on the weak forms a FE solution is initially developed for the single layer. The degrees of freedom (DoFs) of the resultant four-noded generic piezo-elastic single layer FE are then "regenerated" into an equivalent eight-node 3-D formulation in order to allow through-the-thickness assemblage of displacements and stresses, yielding a partially refined multilayer FE assuring displacement and shear stress interlayer continuity and homogeneous shear stress conditions at the outer surfaces. The shear stresses DoFs are dynamically condensed and the FE is reduced to a displacement-based form. The viscoelastic damping behavior is considered at the global FE model level by means of a Laplace transformed ADF model. The active control of vibration is shortly discussed and a set of indices to quantify the damping performance and the individual contributions of the different mechanisms are proposed.